Browsing by Author "Li, Ming-Chia"

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A simple Proof for persistence of snap-back repellers
(2009-04-15)
Li, Ming-Chia
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Lyu, Ming-Jiea
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應用數學系
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Department of Applied Mathematics
In this article, we show that if f has a snap-back repeller then any small C(1) perturbation of f has a snap-back repeller, and hence has Li-Yorke chaos and positive topological entropy, by simply using the implicit function theorem. We also give some examples. (C) 2008 Elsevier Inc. All rights reserved.
Alkali Metal Ion-enhanced Threading of a Perylenediimide-ound Polymer Chain through a Double-stranded Spiroborate Helicate with a Bisporphyrin Unit
(2017-07-01)
Ousaka, Naoki
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Yamamoto, Shinya
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Hayashi, Naoki
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Li, Ming-Chia
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Ho, Rong-Ming
Threading of a poly(ethylene glycol) (PEG) chain linked to a perylenediimide unit at one end with a bulky stopper at the other end through an inner cavity of a bisporphyrin-based double-stranded spiroborate helicate was remarkably accelerated in a specific solvent, in which the PEG chain enfolded sodium cations coordinating to the negatively charged spiroborate helicate, thus forming a 1: 1 inclusion complex with the perylenediimide sandwiched between the bisporphyrin unit.
An Elementary Proof of a Generalization of Banach's Mapping Theorem
(2014-05-01)
Li, Ming-Chia
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應用數學系
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Department of Applied Mathematics
We give an elementary proof of a generalization of Banach's mapping theorem, which says that for any two mappings f : A -> B and g : B -> A, there exists a subset A(0) of A such that g(B\f (A(0))) = A\A(0).
An Elementary Proof of a Generalization of Banach\'s Mapping Theorem
(2014-05-01)
Li, Ming-Chia
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應用數學系
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Department of Applied Mathematics
We give an elementary proof of a generalization of Banach\'s mapping theorem, which says that for any two mappings f : A -> B and g : B -> A, there exists a subset A(0) of A such that g(Bf (A(0))) = AA(0).
Approximation of entropy on hyperbolic sets for one-dimensional maps and their multidimensional perturbations
(2010-06-01)
Li, Ming-Chia
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Malkin, M. I.
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應用數學系
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Department of Applied Mathematics
We consider piecewise monotone (not necessarily, strictly) piecewise C (2) maps on the interval with positive topological entropy. For such a map f we prove that its topological entropy h (top)(f) can be approximated (with any required accuracy) by restriction on a compact strictly f-invariant hyperbolic set disjoint from some neighborhood of prescribed set consisting of periodic attractors, nonhyperbolic intervals and endpoints of monotonicity intervals. By using this result we are able to generalize main theorem from [1] on chaotic behavior of multidimensional perturbations of solutions for difference equations which depend on two variables at nonperturbed value of parameter.
Asymptotic synchronization of modified logistic hyper-chaotic systems and its applications
(2009-04-01)
Chang, Shu-Ming
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Li, Ming-Chia
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Lin, Wen-Wei
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應用數學系
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Department of Applied Mathematics
In this paper, we propose a Modified Logistic Map (MLM) and give a theoretical proof to show that the MLM is a chaotic map according to Devaney's definition. The MLM not only has no chaotic window but is also uniformly distributed in [0, 1] for gamma >= 4. Furthermore, on the basis of the MLMs, we establish a Modified Logistic Hyper-Chaotic System (MLHCS) and apply the MLHCS to develop a symmetric cryptography algorithm, Asymptotic Synchronization of the Modified Logistic Hyper-Chaotic System (ASMLHCS). In our numerical simulation, we analyze the spectra of waveforms of sequences generated from the MLM, showing that the orbit forms a uniform distribution in [0, 1]. In addition, we compute the Poincare recurrences which indicate that the MLM possesses a positive topological entropy. (C) 2007 Elsevier Ltd. All rights reserved.
Breath figure method for construction of high-aspect-ratio pores using diacetylene-labeled polystyrene
(2018-08-19)
Wang, Cheng-Heng
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Chang, Chung-Kai
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Li, Ming-Chia
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交大名義發表
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生物科技學系
Chaos for implicit difference equations with snap-back repellers
(2018-01-01)
Chen, Hung-Ju
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Li, Ming-Chia
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Lin, Shi-Xuan
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應用數學系
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Department of Applied Mathematics
This paper is a study of chaos for generalized dynamical systems derived from implicit difference equations. We define a snap-back repeller for an implicit difference equation and show that its existence implies chaotic dynamics for all small C-1-perturbed systems. By chaotic dynamics, we mean that the solution set of an implicit difference equation contains a compact subset on which the Bernoulli shift map is invariant and has positive topological entropy.
Chaotic difference equations in two variables and their multidimensional perturbations
(2008-05-01)
Juang, Jonq
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Li, Ming-Chia
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Malkin, Mikhail
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應用數學系
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Department of Applied Mathematics
We consider difference equations Phi(lambda)(y(n), y(n+1), . . . , y(n+m)) = 0, n is an element of Z, of order m with parameter. close to that exceptional value lambda(0) for which the function Phi depends on two variables: Phi(lambda 0)(x(0), . . . , x(m)) = xi (x(N), x(N+L)) with 0 <= N, N + L <= m. It is also assumed that for the equation xi(x, y) = 0, there is a branch y = phi(x) with positive topological entropy h(top)(phi). Under these assumptions we prove that in the set of bi-infinite solutions of the difference equation with. in some neighbourhood of lambda(0), there is a closed ( in the product topology) invariant set to which the restriction of the shift map has topological entropy arbitrarily close to htop(phi)/vertical bar L vertical bar, and moreover, orbits of this invariant set depend continuously on. not only in the product topology but also in the uniform topology. We then apply this result to establish chaotic behaviour for Arneodo-Coullet-Tresser maps near degenerate ones, for quadratic volume preserving automorphisms of R(3) and for several lattice models including the generalized cellular neural networks (CNNs), the time discrete version of the CNNs and coupled Chua's circuit.
Chaotic dynamics in a monetary economy with habit persistence
(2008-02-01)
Chen, Hung-Ju
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Li, Ming-Chia
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應用數學系
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Department of Applied Mathematics
This paper develops a cash-in-advance model for persistent habits of consumption. With a binding cash-in-advance constraint, the economic transition can be represented by a one-dimensional or two-dimensional dynamical system, depending on persistent habits of only cash-goods consumption or both cash-goods and credit-goods consumption, respectively. We verify the existence of entropic chaos and ergodic chaos for the former case and identify the presence of entropic chaos for the latter. (C) 2006 Elsevier B.V. All rights reserved.
Chaotic dynamics in an overlapping generations model with myopic and adaptive expectations
(2008-07-01)
Chen, Hung-Ju
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Li, Ming-Chia
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Lin, Yung-Ju
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應用數學系
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Department of Applied Mathematics
In this paper, we study dynamic behavior of an overlapping generations model under three different expectations: perfect foresight, myopic expectations and adaptive expectations. We show that economic transition under myopic or adaptive expectations is very different from that under perfect foresight. When agents are perfectly foresighted, dynamics is simple, with a unique steady state that is globally attracting. However, cycles and chaotic motion can appear under myopic and adaptive expectations. We study the possibility of Li-Yorke chaos under myopic expectations and entropic chaos under adaptive expectations. (C) 2007 Elsevier B.V. All rights reserved.
Child allowances, fertility, and chaotic dynamics
(2013-06-01)
Chen, Hung-Ju
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Li, Ming-Chia
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應用數學系
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Department of Applied Mathematics
This paper analyzes the dynamics in an overlapping generations model with the provision of child allowances. Fertility is an increasing function of child allowances and there exists a threshold effect of the marginal effect of child allowances on fertility. We show that if the effectiveness of child allowances is sufficiently high, an intermediate-sized tax rate will be enough to generate chaotic dynamics. Besides, a decrease in the inter-temporal elasticity of substitution will prevent the occurrence of irregular cycles. (C) 2013 AIP Publishing LLC
Chirality Control and Its Memory at Microphase-Separated Interface of Self-Assembled Chiral Block Copolymers for Nanostructured Chiral Materials
(2017-09-01)
Li, Ming-Chia
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Ousaka, Naoki
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Wang, Hsiao-Fang
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Yashima, Eiji
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Ho, Rong-Ming
Here, we show the induced chirality of an achiral chromophoric dye as a joint of polylactide-containing chiral block copolymers (BCPs*) driven by self-assembly, giving the achiral dyes preferentially arranged in a one-handed helical array at the microphase-separated interface. This helical arrangement of the achiral dyes can be "memorized" after hydrolysis of the polylactides in the BCPs* and serves as a chiral template for further chirality induction of different achiral dyes, probably through attractive aromatic pi-pi interactions at the interface, producing nanostructured chiral materials with tunable circular dichroism signals at desired wavelengths.
Coexistence of invariant sets with and without SRB measures in Henon family
(2010-09-01)
Kiriki, Shin
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Li, Ming-Chia
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Soma, Teruhiko
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應用數學系
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Department of Applied Mathematics
Let {f(a,b)} be the (original) Henon family. In this paper, we show that, for any b near 0, there exists a closed interval J(b) which contains a dense subset J' such that, for any a is an element of J', f(a,b) has a quadratic homoclinic tangency associated with a saddle fixed point of f(a,b) which unfolds generically with respect to the one-parameter family {f(a,b)}(a is an element of Jb). By applying this result, we prove that J(b) contains a residual subset A(b)((2)) such that, for any a is an element of A(n)((2)), f(a,b) admits the Newhouse phenomenon. Moreover, the interval Jb contains a dense subset (A) over tilde (b) such that, for any a is an element of (A) over tilde (b), f(a,b) has a large homoclinic set without SRB measure and a small strange attractor with SRB measure simultaneously.
Competitive Interactions of pi-pi Junctions and Their Role on Microphase Separation of Chiral Block Copolymers
(2017-05-23)
Wen, Tao
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Lee, Jing-Yu
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Li, Ming-Chia
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Tsai, Jing-Cherng
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Hoy, Rong-Ming
Herein, enantiomeric polylactide-containing chiral block copolymers (BCPs*) with aliphatic and aromatic junctions are designed and synthesized for investigating the impact of junction pi-pi interactions on the self-assembly of BCPs*. A profound effect on the microphase separation of the BCP* can be found by introducing the pi-pi interaction of junctions, resulting in reduced structural ordering due to the mixing of constituted blocks by the formation of junction pi-stacking. An ordered microphase-separated structure of the BCP* can be obtained by decreasing the number of aromatic rings of the junction or increasing the total molecular weight of the BCP*. Accordingly, competitive interactions of pi-pi junctions and microphase separation of the BCP* can be manifested by tuning the thermodynamic driving force for self-organization through molecular design. Most interestingly, the self-assembled morphology can be amended by self-assembling the BCP* from solution through the kinetic control of solvent evaporation. Fast solvent evaporation limits the formation of junction stacking while slow solvent evaporation enhances the stacking between junctions, and thus depresses the microphase separation of BCPs*. The self-assembled mechanisms are further evidenced by spectroscopic results and the corresponding induced circular dichroism (ICD) behaviors of the aromatic junctions. This work demonstrates a new approach to thermodynamically and kinetically regulate the self-assembled morphologies of BCP* by introducing the competitive interactions of pi-pi junctions on self-assembly.
Covering relations and Lyapunov condition for topological conjugacy
(2016-01-02)
Li, Ming-Chia
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Lyu, Ming-Jiea
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應用數學系
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Department of Applied Mathematics
In this paper, we study stability of non-autonomous discrete dynamical systems. For a two-sided non-autonomous systems with covering relations determined by a transition matrix A, we show that any small C-0 perturbed system has a sequence of compact invariant sets restricted to which the system is topologically semi-conjugate to sigma(A), the two-sided subshift of finite type induced by A. Together with Lyapunov condition of good rate, the semi-conjugacy will become conjugacy. Moreover, if the Lyapunov condition is strict and has perfect rate, then any small C-1 perturbed systems is topological conjugate to sigma(A). We also study topological chaos of one-sided systems and systems with limit functions. Lack of hyperbolicity and the time dependence of the rate prevent us from applying classical hyperbolic results or earlier works for autonomous systems: cone condition and Lyapunov function. Two examples are provided to demonstrate the existence of a non-trivial, non-hyperbolic invariant and essential of controlling rate.
Covering relations for coupled map networks
(2012-12-01)
Bunimovich, Leonid
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Li, Ming-Chia
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Lyu, Ming-Jiea
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應用數學系
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Department of Applied Mathematics
In this paper, we study coupled map networks over arbitrary finite graphs. An estimate from below for a topological entropy of a perturbed coupled map network is obtained via a topological entropy of an unperturbed network by making use of the covering relations for coupled map networks. The result is quite general; in particular, nonlinear coupling is allowed and no assumptions of hyperbolicity of the local dynamics are made. (C) 2012 Elsevier Inc. All rights reserved.
Criteria on existence of horseshoes near homoclinic tangencies of arbitrary orders
(2018-01-01)
Gonchenko, Sergey
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Li, Ming-Chia
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Malkin, Mikhail
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應用數學系
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Department of Applied Mathematics
Consider (m + 1)-dimensional, m 1, diffeomorphisms that have a saddle fixed point O with m-dimensional stable manifold W-s(O), one-dimensional unstable manifold W-u(O), and with the saddle value sigma different from 1. We assume that W-s(O) and W-u(O) are tangent at the points of some homoclinic orbit and we let the order of tangency be arbitrary. In the case when sigma < 1, we prove necessary and sufficient conditions of existence of topological horseshoes near homoclinic tangencies. In the case when sigma > 1, we also obtain the criterion of existence of horseshoes under the additional assumption that the homoclinic tangency is simple.
Elongation of Axon Extension for Human iPSC-Derived Retinal Ganglion Cells by a Nano-Imprinted Scaffold
(2017-09-01)
Yang, Tien-Chun
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Chuang, Jen-Hua
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Buddhakosai, Waradee
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Wu, Wen-Ju
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Lee, Chen-Ju
Optic neuropathies, such as glaucoma and Leber's hereditary optic neuropathy (LHON) lead to retinal ganglion cell (RGC) loss and therefore motivate the application of transplantation technique into disease therapy. However, it is a challenge to direct the transplanted optic nerve axons to the correct location of the retina. The use of appropriate scaffold can promote the proper axon growth. Recently, biocompatible materials have been integrated into the medical field, such as tissue engineering and reconstruction of damaged tissues or organs. We, herein, utilized nano-imprinting to create a scaffold mimicking the in vitro tissue microarchitecture, and guiding the axonal growth and orientation of the RGCs. We observed that the robust, long, and organized axons of human induced pluripotent stem cell (iPSC)-derived RGCs projected axially along the scaffold grooves. The RGCs grown on the scaffold expressed the specific neuronal biomarkers indicating their proper functionality. Thus, based on our in vitro culture system, this device can be useful for the neurophysiological analysis and transplantation for ophthalmic neuropathy treatment.
Environmental tax policy, habit formation and nonlinear dynamics
(2011-02-01)
Chen, Hung-Ju
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Li, Ming-Chia
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應用數學系
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Department of Applied Mathematics
In this paper, we study the impact of environmental tax policy on the dynamic property in an environment-growth model (John and Pecchenino 1994)[3]. We assume that the government levies consumption tax and uses the tax revenue to improve environmental quality. We show that the economic dynamics can be represented by a first-order difference equation in environmental quality when there is no habit formation of environmental quality. If agents have habit formation of environmental quality, the economic dynamics will be represented by a second-order difference equation in environmental quality. In both cases, chaotic and cyclical fluctuations may exist if agents' preference towards environmental quality, the maintenance efficiency relative to degradation and the tax rate are sufficiently low. However, the economy undergoes transformation from complex dynamics to simple dynamics as the tax rate increases. Furthermore, in the presence of habit formation of environmental quality, an increase in the degree of habit formation lowers the possibility of complex dynamics. (C) 2010 Elsevier Ltd. All rights reserved.